Time-Fractional Order Biological Systems with Uncertain Parameters
暫譯: 不確定參數的時間分數階生物系統
Chakraverty, Snehashish, Jena, Rajarama Mohan, Jena, Subrat Kumar
- 出版商: Morgan & Claypool
- 出版日期: 2020-03-18
- 售價: $2,250
- 貴賓價: 9.5 折 $2,138
- 語言: 英文
- 頁數: 160
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1681737493
- ISBN-13: 9781681737492
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相關分類:
微積分 Calculus、數值分析 Numerical-analysis、物理學 Physics
海外代購書籍(需單獨結帳)
商品描述
The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, λμ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters.
However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge.
In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.
商品描述(中文翻譯)
分數微積分的主題在過去三十年中獲得了相當大的普及和重要性,主要是因為它在各個科學和工程領域的應用得到了驗證。它是對普通微分和積分的推廣,擴展到任意(非整數)階。分數導數已被應用於各種物理問題,例如結構的頻率依賴阻尼行為、生物系統、牛頓流體中板的運動、用於動態系統控制的模糊控制器等。獲得相關的非線性偏微分方程的解(無論是解析解還是數值解)是具有挑戰性的。因此,在過去幾十年中,許多注意力都集中在這類問題的解決上。其他研究者已開發出不同的方法來分析上述問題,並針對精確(確定)參數進行研究。
然而,在生物問題等現實應用中,由於測量/實驗、觀察和其他許多錯誤,並不總是能夠獲得相關參數的確切值。因此,相關的參數和變數可能被視為不確定的。在這裡,不確定性被視為區間/模糊的。因此,開發適當的高效方法並將其應用於解決上述不確定問題是當前的挑戰。
鑒於上述情況,本書是一個新的嘗試,旨在嚴謹地呈現各種模糊(和區間)時間分數動態模型,並針對不同的生物系統使用計算效率高的方法。作者相信本書將對全球的本科生、研究生、研究人員、業界、教職員及其他人員有所幫助。